Skip to main content
Book cover
  • Book
  • © 2017

Formal Methods for Discrete-Time Dynamical Systems

Authors:

  1. Calin Belta

    1. Boston University, Mechanical Engineering, Electrical and Computer Engineering, and Systems Engineering, Boston, USA

    View author publications

    You can also search for this author in PubMed   Google Scholar

  2. Boyan Yordanov

    1. Microsoft Research Ltd, Biological Computation Group, Cambridge, United Kingdom

    View author publications

    You can also search for this author in PubMed   Google Scholar

  3. Ebru Aydin Gol

    1. Middle East Technical University, Department of Computer Engineering, Cankaya, Turkey

    View author publications

    You can also search for this author in PubMed   Google Scholar

  • Provides a self-contained exposition of temporal logic control for finite nondeterministic systems, which are useful even for seasoned formal methods researchers

  • Presents formal verification and control algorithms for discrete-time dynamical systems

  • Intended for a broad audience of scientists and engineers interested in formal methods and controls

  • Includes supplementary material: sn.pub/extras

Part of the book series: Studies in Systems, Decision and Control (SSDC, volume 89)

Sections

eBook USD 149.00
Price excludes VAT (USA)
  • ISBN: 978-3-319-50763-7
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book USD 199.99
Price excludes VAT (USA)
Hardcover Book USD 199.99
Price excludes VAT (USA)
Learn about institutional subscriptions

This is a preview of subscription content, access via your institution.

Table of contents (12 chapters)

  1. Front Matter

    Pages i-xviii
    PDF

  2. Transition Systems, Automata, and Temporal Logics

    1. Front Matter

      Pages 1-1
      PDF

    2. Transition Systems

      • Calin Belta, Boyan Yordanov, Ebru Aydin Gol
      Pages 3-25

    3. Temporal Logics and Automata

      • Calin Belta, Boyan Yordanov, Ebru Aydin Gol
      Pages 27-38

  3. Analysis and Control of Finite Transition Systems

    1. Front Matter

      Pages 39-39
      PDF

    2. Model Checking

      • Calin Belta, Boyan Yordanov, Ebru Aydin Gol
      Pages 41-46

    3. Largest Finite Satisfying Region

      • Calin Belta, Boyan Yordanov, Ebru Aydin Gol
      Pages 47-79

    4. Finite Temporal Logic Control

      • Calin Belta, Boyan Yordanov, Ebru Aydin Gol
      Pages 81-108

  4. Analysis and Control of Discrete-Time Dynamical Systems

    1. Front Matter

      Pages 109-109
      PDF

    2. Discrete-Time Dynamical Systems

      • Calin Belta, Boyan Yordanov, Ebru Aydin Gol
      Pages 111-118

    3. Largest Satisfying Region

      • Calin Belta, Boyan Yordanov, Ebru Aydin Gol
      Pages 119-139

    4. Parameter Synthesis

      • Calin Belta, Boyan Yordanov, Ebru Aydin Gol
      Pages 141-161

    5. Temporal Logic Control

      • Calin Belta, Boyan Yordanov, Ebru Aydin Gol
      Pages 163-183

    6. Finite Bisimulations

      • Calin Belta, Boyan Yordanov, Ebru Aydin Gol
      Pages 185-204

    7. Language Guided Controller Synthesis

      • Calin Belta, Boyan Yordanov, Ebru Aydin Gol
      Pages 205-230

    8. Optimal Temporal Logic Control

      • Calin Belta, Boyan Yordanov, Ebru Aydin Gol
      Pages 231-256

  5. Back Matter

    Pages 257-284
    PDF
Back to top

About this book

This book bridges fundamental gaps between control theory and formal methods. Although it focuses on discrete-time linear and piecewise affine systems, it also provides general frameworks for abstraction, analysis, and control of more general models.

The book is self-contained, and while some mathematical knowledge is necessary, readers are not expected to have a background in formal methods or control theory. It rigorously defines concepts from formal methods, such as transition systems, temporal logics, model checking and synthesis. It then links these to the infinite state dynamical systems through abstractions that are intuitive and only require basic convex-analysis and control-theory terminology, which is provided in the appendix. Several examples and illustrations help readers understand and visualize the concepts introduced throughout the book.

Back to top

Keywords

  • Formal Methods
  • Verification
  • Synthesis
  • Control
  • Hybrid Systems
  • complexity
Back to top

Reviews

“This work is suitable both for researchers from these fields, and also young graduates, provided they are familiar with fundamental concepts of systems theory and theoretical computer science. A strong feature of this work is its plethora of examples, which greatly help in understanding the presented theory, and also help the reader get an idea for the applications that can be considered.” (Lazaros Moysis, zbMATH 1409.93003, 2019)



“The book under review gives an introduction to and overview of particular verification methods for models of systems that evolve in discrete time and usually have unbounded state spaces. … The book can serve as a textbook for an advanced and specialised graduate course in formal methods or control theory.” (Martin Lange, Mathematical Reviews, February, 2018)
Back to top

Authors and Affiliations

  • Boston University, Mechanical Engineering, Electrical and Computer Engineering, and Systems Engineering, Boston, USA

    Calin Belta

  • Microsoft Research Ltd, Biological Computation Group, Cambridge, United Kingdom

    Boyan Yordanov

  • Middle East Technical University, Department of Computer Engineering, Cankaya, Turkey

    Ebru Aydin Gol

Back to top

Bibliographic Information

  • Book Title: Formal Methods for Discrete-Time Dynamical Systems

  • Authors: Calin Belta, Boyan Yordanov, Ebru Aydin Gol

  • Series Title: Studies in Systems, Decision and Control

  • DOI: https://doi.org/10.1007/978-3-319-50763-7

  • Publisher: Springer Cham

  • eBook Packages: Engineering, Engineering (R0)

  • Copyright Information: Springer International Publishing AG 2017

  • Hardcover ISBN: 978-3-319-50762-0Published: 17 March 2017

  • Softcover ISBN: 978-3-319-84485-5Published: 21 July 2018

  • eBook ISBN: 978-3-319-50763-7Published: 08 March 2017

  • Series ISSN: 2198-4182

  • Series E-ISSN: 2198-4190

  • Edition Number: 1

  • Number of Pages: XVIII, 284

  • Number of Illustrations: 54 b/w illustrations, 39 illustrations in colour

  • Topics: Control and Systems Theory, Applied Dynamical Systems, Systems Theory, Control

Back to top
Access via your institution
eBook USD 149.00
Price excludes VAT (USA)
  • ISBN: 978-3-319-50763-7
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book USD 199.99
Price excludes VAT (USA)
Hardcover Book USD 199.99
Price excludes VAT (USA)
Learn about institutional subscriptions